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Decide whether function exists

Source: 51 Polish MO 2000 Second Round - Problem 5

April 23, 2018
algebranumber theoryfunctionPoland

Problem Statement

Decide whether exists function f:N→Nf: \mathbb{N} \rightarrow \mathbb{N}, such that for each n∈Nn \in \mathbb{N} is f(f(n))=2nf(f(n) )= 2n.
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